Tuesday, January 13, 2015

SHM Chapter 24 x vs f resonance graph

The response of the oscillatory system depends on the value of the frequency of the periodic force (also known as the “driving” frequency).                LO (k)


When the driving frequency is close to or equal to the natural frequency fo of the oscillating system, maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude.  This phenomenon is called resonance.      

 A more accurate and complicated picture could be found on Wikipedia.



   
This computer model can be used to generate a similar data representation when using the instruction found on the html below the model.


Case: b=0 no damping.
All 100 spring mass systems oscillates forever without coming to rest. Notice when the ratio of driving frequency to natural frequency fo of the oscillating system  f/fo = 1  maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude (extended beyond 10).  This phenomenon is called resonance. 
  
Case 1: b=0.1 very light damping
Notice when the ratio of driving frequency to natural frequency fo of the oscillating system  f/fo = 1  maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude (equal 10 m).  This phenomenon is called resonance. 



Case2: b=0.3 light damping
Notice when the ratio of driving frequency to natural frequency fo of the oscillating system  f/fo slightly less than 1,  maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude (about 3.3).  This phenomenon is called resonance. 



Case3: b =0.6 moderate damping

Notice when the ratio of driving frequency to natural frequency fo of the oscillating system  f/fo slightly less than 1 about 0.9 in this case,  maximum energy is transferred from the periodic force (driver) to the oscillating system which will vibrate with maximum amplitude (about 1.8).  This phenomenon is called resonance.


Case4: b = 2.0 critical damping
Notice the resonance does not occur anymore. 



Case5: very heavy damping
Notice the resonance does not occur anymore. 

Model:

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM24/SHM24_Simulation.xhtml

YouTube explanation:

http://youtu.be/Tn-NmpMX_z0
  

Journal paper:




arXiv:1501.01535 [pdf]




Understanding resonance graphs using Easy Java Simulations (EJS) and why we use EJS
Comments: 6 pages, 8 figures, Physics Education Journal